Log24

Monday, December 2, 2019

Aesthetics at Harvard

Filed under: General — Tags: , , — m759 @ 4:05 PM

"What the piece of art is about is the gray space in the middle."

— David Bowie, as quoted in the above Crimson  piece.

Bowie's "gray space" is the space between the art and the beholder.

I prefer the gray space in the following figure —

Some small Galois spaces (the Cullinane models)

Context:  The Trinity Stone  (Log24, June 4, 2018).

Wednesday, November 20, 2019

Winners for Losers

Filed under: General — Tags: — m759 @ 7:42 PM

After Rothko

Filed under: General — Tags: , — m759 @ 12:52 PM

RED
_____________________________________________________________________________


 

GRAY
______________________


Arya on Rothko

Monday, August 26, 2019

Firsts:  Farmer’s Daughter

Filed under: General — Tags: — m759 @ 11:45 AM

See as well the firsts of Sophia Lillis (Saturday, August 24).

Wednesday, August 21, 2019

Spring-Loaded

Filed under: General — Tags: — m759 @ 10:00 AM

Continued  (from previous post) . . .

British cover (2011) for 'From Eternity to Here,' by Sean Carroll

Saturday, August 17, 2019

Crystalline Complexity

Filed under: General — Tags: — m759 @ 6:08 PM

Burroway on Hustvedt in The New York Times ,
Sunday, March 9, 2003 —

See as well "Putting the Structure  in Structuralism."

Tuesday, July 23, 2019

Gate of Heavenly Peace

Filed under: General — Tags: — m759 @ 11:29 AM

Wikipedia — 

"The Tian'anmen (also Tiananmen or Tienanmen)
([tʰjɛ́n.án.mə̌n]), or the Gate of Heavenly Peace, is
a monumental gate in the centre of Beijing, widely
used as a national symbol of China. First built during
the Ming dynasty in 1420, Tiananmen was the entrance
to the Imperial City . . . ."

A related article on Chinese history, The Critical Moment,
suggests an associated (if only by title) webpage —

See as well The Painted Word .

Wednesday, May 15, 2019

A Wrinkle in Time and Space

Filed under: General — Tags: — m759 @ 11:32 AM

Or:  Tom Wolfe in the Quantum Realm

Related posts: Search Log24 for Bubble.

Saturday, May 4, 2019

The Long Strange Trip of Abstract Art

Filed under: General — Tags: , — m759 @ 9:23 PM

In memory of an art collector's April 24 death —

See also Log24 on April 24

Friday, March 29, 2019

The Blazon World*

Filed under: General — m759 @ 4:59 PM

“At that instant he saw, in one blaze of light,
an image of unutterable conviction,
the reason why the artist works and lives
and has his being — the reward he seeks —
the only reward he really cares about,
without which there is nothing. It is to snare
the spirits of mankind in nets of magic,
to make his life prevail through his creation,
to wreak the vision of his life, the rude and painful
substance of his own experience, into the congruence
of blazing and enchanted images that are themselves
the core of life, the essential pattern whence
all other things proceed, the kernel of eternity.”

— Thomas Wolfe, Of Time and the River

* Title suggested by that of a Siri Hustvedt novel.
   See also Blazon in this journal.

Friday, March 22, 2019

Charles Jencks’s Grand Unified Theory

Filed under: General — Tags: , , — m759 @ 2:00 PM

"The stars and galaxies seem static, eternal, or moving slowly
in deterministic patterns, becoming the background stage
on which we move. But if we could speed up the sequence,
we would see how dramatic and unpredictable this background
really is — an actor, director, script and stage all at once.
Moreover, it is a unified universe, a single unfolding event
of which we are an embedded part, a narrative of highly
dangerous and fine-tuned events, something more like
a detective thriller with many crimes and last-minute escapes
than the impersonal account of astronomy textbooks.
We are only just beginning to decipher the plot and figure out
the Cosmic Code, as Heinz Pagels puts it."

— Charles Jencks, The Architecture of the Jumping Universe :
A Polemic
  (How Complexity Science is Changing Architecture
and Culture), Academy Editions, 1995, rev. ed. 1997

"A Grand Unified Theory (GUT) is a model in particle physics…."
Wikipedia

"Under the GUT symmetry operation these field components
transform into one another. The reason quantum particles 
appear to have different properties in nature is that the unifying
symmetry is broken. The various gluons, quarks and leptons
are analogous to the facets of a cut diamond, which appear
differently according to the way the diamond is held but in
fact are all manifestations of the same underlying object."

— Heinz Pagels, Perfect Symmetry , Bantam paperback, 1986, p. 284

See also the recent post Multifaceted Narrative.

Thursday, October 25, 2018

Clerisy

Filed under: General — Tags: , — m759 @ 1:18 PM

Two images from a post of April 11, 2014

Tom Cruise at the Vatican in MI3

_____________________________________________________________________

Michelle Monaghan, star of "The Path," in MI3 —

Hickory Dickory.

Saturday, September 22, 2018

The Venturi Manifesto

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 1:00 PM

Venturi reportedly died on Tuesday, September 18.*

See also this journal on that date.

* Fact check:

Tuesday, September 11, 2018

Art-Historical Narrative

Filed under: General — Tags: , — m759 @ 2:40 PM

Art history from Galerie St. Etienne

Summer Solstice Notes

Wednesday, September 5, 2018

Midnight Art

Filed under: General — Tags: — m759 @ 3:03 AM

http://www.log24.com/log/pix18/180905-Art-overarching_narrative-Tablet.gif

See also 12 AM Sept. 4 in this  journal, "Identity Crisis."

Related material — "Overarching" in this journal.

Update of 4:12 AM ET —

The name of the New Yorker  artist in the Identity Crisis post,
Tamara Shopsin, has now been added to the illustrated excerpt.

See as well . . .

https://www.nytimes.com/2018/09/04/obituaries/
kenny-shopsin-dead.html
.

itemprop="datePublished" 
content="2018-09-04T22:17:59.000Z"

Friday, August 24, 2018

The Wandelweiser Manifesto

Filed under: General — Tags: — m759 @ 5:35 PM

Or:  Signpost of Change

From a cartoon graveyard

http://www.log24.com/log/pix18/180824-Outre_Tinkering-NYer-Aug-27-2018-issue-p84.jpg

Backstory

Alex Ross on Wandelweiser, September 2016

Tuesday, July 17, 2018

Deep Learning for Jews

Filed under: General — Tags: , — m759 @ 12:23 PM

From The New York Times  on June 20, 2018 —

" In a widely read article published early this year on arXiv.org,
a site for scientific papers, Gary Marcus, a professor at
New York University, posed the question:

'Is deep learning approaching a wall?'

He wrote, 'As is so often the case, the patterns extracted
by deep learning are more superficial than they initially appear.' "

See as well an image from posts tagged Quantum Suffering  . . .

The time above, 10:06:48 PM July 16, is when  I saw

"What you mean 'we,' Milbank?"

Sunday, July 15, 2018

Fashion Statements

Filed under: General — Tags: — m759 @ 1:00 AM

See Glad Rags in this journal.

Bill Haley, not Michael J. Fox, was my  experience of 1955.

Thursday, July 12, 2018

The Bell

Filed under: General — Tags: , — m759 @ 6:11 PM

Three hidden keys open three secret gates
Wherein the errant will be tested for worthy traits
And those with the skill to survive these straits
Will reach The End where the prize awaits

— Ready Player One , by Ernest Cline

"Look, my favorite expression is,
'When you go up to the bell, ring it,
or don’t go up to the bell.'
We’ve gone too far. We have to ring the bell."

Mel Brooks on "The Producers"
     in The New York Times  today.

A 2016 Scribner edition of Stephen King's IT —

Related material —

Mystery box  merchandise from the 2011  J. J. Abrams film  Super 8 

Saturday, July 7, 2018

Easter Eggs for Rosalind

Filed under: General — Tags: — m759 @ 1:19 PM

Three hidden keys open three secret gates
Wherein the errant will be tested for worthy traits
And those with the skill to survive these straits
Will reach The End where the prize awaits

Ready Player One , by Ernest Cline

Related text —

Tu es Petrus et super hanc petram
aedificabo ecclesiam meam et tibi
dabo claves regni caelorum
 

Mt. 16:18

Related imagery —

From Steven Spielberg's film "Ready Player One" (2018) —

From this journal on June 17, 2003

From The New York Times  on Easter night, 2007 —

Death of Sol LeWitt

See as well Rosalind Krauss on LeWitt:

Tuesday, July 3, 2018

The Ant and the WASP

Filed under: General — Tags: , — m759 @ 4:56 PM

See also posts tagged "Lost" and a search for "Excellent Adventure."

Monday, May 28, 2018

Epstein on Art

Filed under: General — Tags: — m759 @ 2:16 PM

Joseph Epstein in the online Weekly Standard
on May 24, 2018, at 3:03 PM —

Hilton Kramer, in a powerful essay called “Revenge of the Philistines,” praised Wolfe’s account of the sociology of the visual art of the time. On the comedy inherent in the subject, he noted, Wolfe “is illuminating and often hilarious.” Yet, when it came to the analysis of ideas, Kramer felt, “when it comes down to actual works of art and the thinking they both embody and inspire, Wolfe is hopelessly out of his depth . . . and, no doubt, beyond his true interests.” He faulted Wolfe for his inability to understand the historical context of the contemporary situation in art or how we have come to where we are in a way that carries us well beyond “the drawing-room comedy of The Painted Word .” Kramer concluded: “It is this fundamental incomprehension of the role of criticism in the life of art—this enmity to the function of theory in the creation of culture—that identifies The Painted Word , despite its knowingness and its fun, as a philistine utterance, an act of revenge against a quality of mind it cannot begin to encompass and must therefore treat as a preposterous joke.”

For Kramer in greater depth, see an online biography.

Friday, May 18, 2018

Central Square

Filed under: General — Tags: — m759 @ 11:54 AM

This  journal 10 years ago today  had a link to a post on
Tom Wolfe's "Sorry, but Your Soul Just Died."

Thursday, May 17, 2018

Leap

Filed under: General — Tags: — m759 @ 9:45 PM

Quoted here on May 5, 2018

" Lying at the axis of everything, zero is both real and imaginary. Lovelace was fascinated by zero; as was Gottfried Leibniz, for whom, like mathematics itself, it had a spiritual dimension. It was this that let him to imagine the binary numbers that now lie at the heart of computers: 'the creation of all things out of nothing through God's omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing.' He also wrote, 'The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and nonbeing.' "

— A footnote from page 229 of Sydney Padua's
    April 21, 2015, book on Lovelace and Babbage

The page number  229 may also be interpreted, cabalistically,
as the date  2/29, Leap Day.

See Leap Day 2016 among the posts tagged Mind Spider.

Speak, Memory

Filed under: General — Tags: — m759 @ 6:29 PM

On the film "Anna" in the previous post

See also the above world premiere date in the posts of October 2013
esp. the post Conundrum.

Related material — An early scene in "Mindscape" . . .

. . . and "The Abacus Conundrum" in this journal.

DATA

Filed under: General — Tags: — m759 @ 5:17 PM

Quoted here on May 7, 2018

Novelist George Eliot and programming pioneer Ada Lovelace —

PBS last night —

Trailer for last night's PBS program on artificial intelligence —

Piano roll for "I am sixteen going on seventeen" (see previous post) —

From yesterday evening's "Strong Women" post

"It's been dirty for dirty
Down the line . . ."

— Joni Mitchell,
"For the Roses" album (1972)

"… for the roses
Had the look of flowers that are looked at.”

— T. S. Eliot, Four Quartets

May 17

Filed under: General — Tags: — m759 @ 3:45 PM

"Well, she was just 17 …" — Song lyric

See as well, from last Christmas Eve, Piano Roll.

Wednesday, May 16, 2018

Strong Women

Filed under: General — Tags: — m759 @ 7:50 PM

Review

Filed under: General — Tags: , — m759 @ 5:52 PM

The title of the previous post, "Church and Temple," together
with today's online New York Times  obituaries for singer 
Lara Saint Paul (d. May 8) and playwright Leah Rose Napolin
(d. May 13), suggests a review

See as well a Log24 search for Isaac Singer.

Church and Temple

Filed under: General — Tags: , , , — m759 @ 10:48 AM

Same Old Story

Filed under: General — Tags: , , — m759 @ 9:00 AM

. . . as time goes by.

Tuesday, May 15, 2018

Space Revisited

Filed under: General — Tags: , — m759 @ 11:32 AM

"Well, let's see now "

— Tom Wolfe, July 18, 2009

Monday, May 14, 2018

Space

Filed under: General,Geometry — Tags: , — m759 @ 10:30 PM

"A generation lost in space" — Don McLean

See as well Varignon in the previous post.

Logos at Harvard

Filed under: General,Geometry — Tags: , — m759 @ 3:01 PM

In 2013, Harvard University Press changed its logo to an abstract "H."

Harvard University Press Logo, Before and After

Both logos now accompany a Harvard video first published in 2012,
"The World of Mathematical Reality." 

In the video, author Paul Lockhart discusses Varignon's theorem
without naming Varignon (1654-1722) . . .

Paul Lockhart on geometry

A related view of "mathematical reality" —

Note the resemblance to Plato's Diamond.

Saturday, May 12, 2018

The McLean Awakening

Filed under: General — Tags: — m759 @ 4:14 PM

"Oh, and there we were all in one place
A generation lost in space"

— "American Pie" by Don McLean

Wednesday, August 30, 2017

Horn and Hard Art

Filed under: General — Tags: , — m759 @ 9:17 PM

Or:   Bee Season  Continues

Click the automat image above to enlarge.
Click the Horn & Hardart image below for the source.

Andreas Feininger, LIFE magazine photos, 1946

See as well Catskills Heaven (Log24 on August 20, 2017) —

The Coen brothers, 2007 screenplay —

(From a novel by Cormac McCarthy)

Tuesday, May 19, 2015

The Lindbergh Manifesto

Filed under: General,Geometry — Tags: , — m759 @ 3:24 AM

"Creation is the birth of something, and
something cannot come from nothing."

— Photographer Peter Lindbergh at his website

From a biography of Lindbergh —

" it took Lindbergh awhile to find his true métier.
Born in Krefeld, Germany, in 1944….
Barely out of his teens, he became a painter who
embraced conceptual art and — for reasons he
has since forgotten — adopted the professional
name « Sultan. »   Lindbergh was a few years
short of his 30th birthday when he turned to
photography."

— "The Man Who Loves Women," by Pamela Young,
Toronto Globe & Mail , September 19, 1996

A Lindbergh work (at right below) from his conceptual-art days —

For a connection between the above work by Paul Talman and the
above "Mono Type 1" of Lindbergh, see…

Friday, February 21, 2014

Night’s Hymn of the Rock

Filed under: General,Geometry — Tags: , , — m759 @ 3:33 AM

One way of interpreting the symbol  IMAGE- Modal Diamond in a square 
at the end of yesterday's post is via
the phrase "necessary possibility."

See that phrase in (for instance) a post
of July 24, 2013, The Broken Tablet .

The Tablet  post may be viewed in light
of a Tom Wolfe passage quoted here on
the preceding day, July 23, 2013—

IMAGE- Tom Wolfe in 'The Painted Word' on conceptual art

On that  day (July 23) another weblog had
a post titled

Wallace Stevens: Night's Hymn of the Rock.

Some related narrative —

IMAGE- The 2001 film 'The Discovery of Heaven'

I prefer the following narrative —

Part I:  Stevens's verse from "The Rock" (1954) —
"That in which space itself is contained"

Part II:  Mystery Box III: Inside, Outside (2014)

Friday, June 29, 2012

The Uploading (continued)*

Filed under: General — m759 @ 9:29 PM

It Must Be Abstract
It Must Change
It Must Give Pleasure

Parts of a poem by Wallace Stevens

“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”

– Thomas WolfeOf Time and the River

      Of Time and the River and the Frogs —

Video uploaded on Jan. 26, 2008, of talk, 'The Lively Kernel,' on object-oriented software

* This post's title refers to the above uploading date—  Jan. 26, 2008.

Monday, July 5, 2010

Window

Filed under: General — Tags: , — m759 @ 9:00 AM

"Examples are the stained-glass
  windows of knowledge." — Nabokov

Image-- Example of group actions on the set Omega of three partitions of a 4-set into two 2-sets

Related material:

Thomas Wolfe and the
Kernel of Eternity

Friday, May 9, 2008

Friday May 9, 2008

Filed under: General,Geometry — Tags: — m759 @ 9:00 AM
Kernel of Eternity
continued from April 29

 
The Klein Group: The four elements in four colors, with black points representing the identity


Wikipedia on the Klein group (denoted V, for Vierergruppe):

In this representation, V is a normal subgroup of the alternating group A4 (and also the symmetric group S4) on 4 letters. In fact, it is the kernel of a surjective map from S4 to S3. According to Galois theory, the existence of the Klein four-group (and in particular, this representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals.

For radicals of another sort, see A Logocentric Meditation, A Mass for Lucero, and Steven Erlanger in The New York Times— "France Still Divided Over Lessons of 1968 Unrest."

The Klein Group as Kernel
of a Map from S4 to S3:

Portrait of O:  The Klein Group as Kernel in  the Symmetric Group of Degree Four

Click to enlarge.

For those who prefer Galois's
politics to his mathematics,
there is
MAY 68: STREET POSTERS
FROM THE PARIS REBELLION

at London's Southbank Centre
 (May 1 – June 1, 2008).

Tuesday, April 29, 2008

Tuesday April 29, 2008

Filed under: General,Geometry — Tags: , , — m759 @ 11:09 AM
Sacerdotal Jargon
at Harvard:

Thomas Wolfe

Thomas Wolfe
(Harvard M.A., 1922)

versus

Rosalind Krauss

Rosalind Krauss
(Harvard M.A., 1964,
Ph.D., 1969)

on

The Kernel of Eternity

"No culture has a pact with eternity."
George Steiner, interview in  
The Guardian of April 19

"At that instant he saw,
in one blaze of light, an image
of unutterable conviction….
the core of life, the essential
pattern whence all other things
proceed, the kernel of eternity."

— Thomas Wolfe, Of Time
and the River, quoted in
Log24 on June 9, 2005

 

From today's online Harvard Crimson:

"… under the leadership of Faust,
Harvard students should look forward
to an ever-growing opportunity for
international experience
and artistic endeavor."

 

Wolfgang Pauli as Mephistopheles

Pauli as Mephistopheles
in a 1932 parody of
Goethe's
Faust at Niels Bohr's
institute in Copenhagen

From a recent book
on Wolfgang Pauli,
The Innermost Kernel:

Pauli's Dream Square (square plus the two diagonals)

A belated happy birthday
to the late
Felix Christian Klein
  (born on April 25) —

The Klein Group: The four elements in four colors, with black points representing the identity

Another Harvard figure quoted here on Dec. 5, 2002:

"The theory of poetry, that is to say, the total of the theories of poetry, often seems to become in time a mystical theology or, more simply, a mystique. The reason for this must by now be clear. The reason is the same reason why the pictures in a museum of modern art often seem to become in time a mystical aesthetic, a prodigious search of appearance, as if to find a way of saying and of establishing that all things, whether below or above appearance, are one and that it is only through reality, in which they are reflected or, it may be, joined together, that we can reach them. Under such stress, reality changes from substance to subtlety, a subtlety in which it was natural for Cézanne to say: 'I see planes bestriding each other and sometimes straight lines seem to me to fall' or 'Planes in color…. The colored area where shimmer the souls of the planes, in the blaze of the kindled prism, the meeting of planes in the sunlight.' The conversion of our Lumpenwelt went far beyond this. It was from the point of view of another subtlety that Klee could write: 'But he is one chosen that today comes near to the secret places where original law fosters all evolution. And what artist would not establish himself there where the organic center of all movement in time and space– which he calls the mind or heart of creation– determines every function.' Conceding that this sounds a bit like sacerdotal jargon, that is not too much to allow to those that have helped to create a new reality, a modern reality, since what has been created is nothing less."

— Wallace Stevens, Harvard College Class of 1901, "The Relations between Poetry and Painting" in The Necessary Angel (Knopf, 1951)

From a review of Rosalind Krauss's The Optical Unconscious  (MIT Press hardcover, 1993):

Krauss is concerned to present Modernism less in terms of its history than its structure, which she seeks to represent by means of a kind of diagram: "It is more interesting to think of modernism as a graph or table than a history." The "table" is a square with diagonally connected corners, of the kind most likely to be familiar to readers as the Square of Opposition, found in elementary logic texts since the mid-19th century. The square, as Krauss sees it, defines a kind of idealized space "within which to work out unbearable contradictions produced within the real field of history." This she calls, using the inevitable gallicism, "the site of Jameson's Political Unconscious" and then, in art, the optical unconscious, which consists of what Utopian Modernism had to kick downstairs, to repress, to "evacuate… from its field."

— Arthur C. Danto in ArtForum, Summer 1993

Rosalind Kraus in The Optical Unconscious (MIT Press paperback, 1994):

For a presentation of the Klein Group, see Marc Barbut, "On the Meaning of the Word 'Structure' in Mathematics," in Introduction to Structuralism, ed. Michael Lane (New York: Basic Books, 1970). Claude Lévi-Strauss uses the Klein group in his analysis of the relation between Kwakiutl and Salish masks in The Way of the Masks, trans. Sylvia Modelski (Seattle: University of Washington Press, 1982), p. 125; and in relation to the Oedipus myth in "The Structural Analysis of Myth," Structural Anthropology, trans. Claire Jackobson [sic] and Brooke Grundfest Schoepf (New York: Basic Books, 1963). In a transformation of the Klein Group, A. J. Greimas has developed the semiotic square, which he describes as giving "a slightly different formulation to the same structure," in "The Interaction of Semiotic Constraints," On Meaning (Minneapolis: University of Minnesota Press, 1987), p. 50. Jameson uses the semiotic square in The Political Unconscious (see pp. 167, 254, 256, 277) [Fredric Jameson, The Political Unconscious: Narrative as a Socially Symbolic Act (Ithaca: Cornell University Press, 1981)], as does Louis Marin in "Disneyland: A Degenerate Utopia," Glyph, no. 1 (1977), p. 64.

For related non-sacerdotal jargon, see…
 

Wikipedia on the Klein group (denoted V, for Vierergruppe):

In this representation, V is a normal subgroup of the alternating group A4 (and also the symmetric group S4) on 4 letters. In fact, it is the kernel of a surjective map from S4 to S3. According to Galois theory, the existence of the Klein four-group (and in particular, this representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals.

For radicals of another sort, see A Logocentric Meditation, A Mass for Lucero, and [update of 7 PM] Steven Erlanger in today's New York Times— "France Still Divided Over Lessons of 1968 Unrest."

For material related to Klee's phrase mentioned above by Stevens, "the organic center of all movement in time and space," see the following Google search:

April 29, 2008, Google search on 'penrose space time'

Click on the above
 image for details.

See also yesterday's
Religious Art.

Thursday, June 21, 2007

Thursday June 21, 2007

Filed under: General,Geometry — Tags: — m759 @ 12:07 PM
Let No Man
Write My Epigraph

(See entries of June 19th.)

"His graceful accounts of the Bach Suites for Unaccompanied Cello illuminated the works’ structural logic as well as their inner spirituality."

Allan Kozinn on Mstislav Rostropovich in The New York Times, quoted in Log24 on April 29, 2007

"At that instant he saw, in one blaze of light, an image of unutterable conviction…. the core of life, the essential pattern whence all other things proceed, the kernel of eternity."

— Thomas Wolfe, Of Time and the River, quoted in Log24 on June 9, 2005

"… the stabiliser of an octad preserves the affine space structure on its complement, and (from the construction) induces AGL(4,2) on it. (It induces A8 on the octad, the kernel of this action being the translation group of the affine space.)"

— Peter J. Cameron, "The Geometry of the Mathieu Groups" (pdf)

"… donc Dieu existe, réponse!"

— Attributed, some say falsely,
to Leonhard Euler
 
"Only gradually did I discover
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"

(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)

 

Wolfgang Pauli as Mephistopheles

"Pauli as Mephistopheles
in a 1932 parody of
Goethe's Faust at Niels Bohr's
institute in Copenhagen.
The drawing is one of
many by George Gamow
illustrating the script."
Physics Today

 

"Borja dropped the mutilated book on the floor with the others. He was looking at the nine engravings and at the circle, checking strange correspondences between them.

'To meet someone' was his enigmatic answer. 'To search for the stone that the Great Architect rejected, the philosopher's stone, the basis of the philosophical work. The stone of power. The devil likes metamorphoses, Corso.'"

The Club Dumas, basis for the Roman Polanski film "The Ninth Gate" (See 12/24/05.)

"Pauli linked this symbolism
with the concept of automorphism."

The Innermost Kernel
 (previous entry)

And from
"Symmetry in Mathematics
and Mathematics of Symmetry
"
(pdf), by Peter J. Cameron,
a paper presented at the
International Symmetry Conference,
Edinburgh, Jan. 14-17, 2007,
we have

The Epigraph–

Weyl on automorphisms
(Here "whatever" should
of course be "whenever.")

Also from the
Cameron paper:

Local or global?

Among other (mostly more vague) definitions of symmetry, the dictionary will typically list two, something like this:

• exact correspondence of parts;
• remaining unchanged by transformation.

Mathematicians typically consider the second, global, notion, but what about the first, local, notion, and what is the relationship between them?  A structure M is homogeneous if every isomorphism between finite substructures of M can be extended to an automorphism of M; in other words, "any local symmetry is global."

Some Log24 entries
related to the above politically
(women in mathematics)–

Global and Local:
One Small Step

and mathematically–

Structural Logic continued:
Structure and Logic
(4/30/07):

This entry cites
Alice Devillers of Brussels–

Alice Devillers

"The aim of this thesis
is to classify certain structures
which are, from a certain
point of view, as homogeneous
as possible, that is which have
  as many symmetries as possible."

"There is such a thing
as a tesseract."

Madeleine L'Engle 

Thursday, June 9, 2005

Thursday June 9, 2005

Filed under: General,Geometry — Tags: — m759 @ 7:45 PM
Kernel of Eternity

continued

"At that instant he saw,
in one blaze of light,
an image of unutterable conviction….
the core of life, the essential pattern
whence all other things proceed,
the kernel of eternity."

— Thomas Wolfe,
Of Time and the River

From "The Relations between
Poetry and Painting," by Wallace Stevens:

"The theory of poetry, that is to say, the total of the theories of poetry, often seems to become in time a mystical theology or, more simply, a mystique. The reason for this must by now be clear. The reason is the same reason why the pictures in a museum of modern art often seem to become in time a mystical aesthetic, a prodigious search of appearance, as if to find a way of saying and of establishing that all things, whether below or above appearance, are one and that it is only through reality, in which they are reflected or, it may be, joined together, that we can reach them. Under such stress, reality changes from substance to subtlety…. It was from the point of view of… [such a] subtlety that Klee could write: 'But he is one chosen that today comes near to the secret places where original law fosters all evolution. And what artist would not establish himself there where the organic center of all movement in time and space—which he calls the mind or heart of creation— determines every function.' Conceding that this sounds a bit like sacerdotal jargon, that is not too much to allow to those that have helped to create a new reality, a modern reality, since what has been created is nothing less."

As yesterday's entry "Kernel of Eternity" indicated, the word "kernel" has a definite meaning in mathematics.  The Klein four-group, beloved of structural anthropologists and art theorists, is a particularly apt example of a kernel. (See PlanetMath for details.)

Diagrams of this group may have influenced Giovanni Sambin, professor of mathematical logic at the University of Padua; the following impressive-looking diagram is from Sambin's

The image “http://www.log24.com/theory/images/SambinBP1Pic2A.jpg” cannot be displayed, because it contains errors.

Sambin argues that this diagram reflects some of the basic structures of thought itself… making it perhaps one way to describe what  Klee called the "mind or heart of creation." 

But this verges on what Stevens called the sacerdotal.  It seems that a simple picture of the "kernel of eternity" as the four-group, a picture without reference to logic or philosophy, and without distracting letters and labels, is required.  The following is my attempt to supply such a picture:

Klein four-group

This is a picture of the four-group
as a permutation group on four points.
Pairs of colored arrows indicate the three
transformations other than the identity,
which may be regarded either as
invisible or as rendered by
the four black points themselves.

Update of 7:45 PM Thursday:

Review of the above (see comments)
by a typical Xanga reader:

"Ur a FUCKIN' LOSER!!!!!  LMFAO!!!!"

For more merriment, see
The Optical Unconscious
and
The Painted Word.

A recent Xangan movie review:

"Annakin's an idiot, but he's not an idiot because that's the way the character works, he's an idiot because George Lucas was too lazy to make him anything else. He has to descend to the Daaaahk Side, but the dark side never really seems all that dark. He kills children, but offscreen. We never get to see the transformation. One minute he cares about the republic, the next he's killing his friends, and then for some reason he's duelling with Obi Wan on a lava flow. Who cares? Not me….

So a big ol' fuck you to George Lucas. Fuck you, George!"

Both Xangans seem to be fluent in what Tom Wolfe has called the "fuck patois."

A related suggestion from Google:

Give Dad a photo gift

These remarks from Xangans and Google
 suggest the following photo gift,
based on a 2003 journal entry:

The image “http://www.log24.com/log/pix05A/050609-Fahne.jpg” cannot be displayed, because it contains errors.

Wednesday, June 8, 2005

Wednesday June 8, 2005

Filed under: General,Geometry — m759 @ 4:00 PM

Kernel of Eternity

Today is the feast day of Saint Gerard Manley Hopkins, “immortal diamond.”

“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”

— Thomas Wolfe, Of Time and the River

“… the stabiliser of an octad preserves the affine space structure on its complement, and (from the construction) induces AGL(4,2) on it. (It induces A8 on the octad, the kernel of this action being the translation group of the affine space.)”

— Peter J. Cameron,
The Geometry of the Mathieu Groups (pdf)

“… donc Dieu existe, réponse!

— attributed, some say falsely, to Leonhard Euler

Sunday, June 8, 2003

Sunday June 8, 2003

Filed under: General — m759 @ 3:04 AM

Of Time and the River

Today is the feast day of Saint Gerard Manley Hopkins, “immortal diamond.”

“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”

Thomas Wolfe, Of Time and the River

Thomas Wolfe

“entered the university at Chapel Hill at fifteen ‘an awkward, unhappy misfit.’ By the time he graduated, he was editor of the college newspaper….”

Jeff MacNelly, who died on this date in the Year of Our Lord 2000,

“in 1977 started drawing the comic strip ‘Shoe‘…. The strip was named in honor of the legendary Jim Shumaker, for whom MacNelly worked at the Chapel Hill Weekly.” 

From my Monday, June 2, 2003 entry:

Two quotations from “The Diamond Project“:

“We all know that something is eternal,” the Stage Manager says. “And it ain’t houses and it ain’t names, and it ain’t earth, and it ain’t even stars—everybody knows in their bones that something is eternal, and that something has to do with human beings.”
— John Lahr, review of “Our Town 

“Set me as a seal upon your heart, as a seal upon your arm; for love is strong as death, passion fierce as the grave.  Its flashes are flashes of fire, a raging flame.”
Song of Solomon

Here are some other thoughts from the same date, but a different time, fictional time, Faulkner time:

June Second, 1910

Where the shadow of the bridge fell I could see down for a long way, but not as far as the bottom. When you leave a leaf in water a long time after a while the tissue will be gone and the delicate fibers waving slow as the motion of sleep. They dont touch one another, no matter how knotted up they once were, no matter how close they lay once to the bones. And maybe when He says Rise the eyes will come floating up too, out of the deep quiet and the sleep, to look on glory.

— William Faulkner, The Sound and the Fury

The concluding link from my June 2, 2003, entry furnishes a clue to the timelessness of Quentin Compson‘s thoughts above:

Glory… Song of Songs 8. 7-8

From the King James Bible‘s rendition of the Song of Songs:

8:7  Many waters cannot quench love, neither can the floods drown it: if a man would give all the substance of his house for love, it would utterly be contemned.
8:8  We have a little sister, and she hath no breasts: what shall we do for our sister in the day when she shall be spoken for?

For Quentin Compson’s thoughts on his little sister Caddy, consult the online hypertext edition of

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